3D meshless modeling of piezoelectric structure based on the radial point interpolation method

Abstract

Piezoelectric materials find widespread applications in high-precision actuators and sensors. However, the traditional finite element method falls short in meeting the simulation needs of piezoelectric structures due to complexities in mesh generation and precision requirements for accurate simulations. This paper focuses on adapting and generalizing the meshless modeling technique based on the radial point interpolation method to address three-dimensional simulations of piezoelectric structures and accurately model positive and inverse piezoelectric behaviors. The piezoelectric body is discretized into point cloud data, and displacement and potential are approximated by interpolating values through the radial point interpolation method. Subsequently, a 3D meshless model for general piezoelectric structures is formulated based on the principle of minimum potential energy. The influences of key factors on interpolation accuracy and computational cost were discussed. Numerical examples, featuring a 3D piezoelectric bimorph beam as actuators and sensors, validate the efficacy of this extended approach. Results affirm that the three-dimensional meshless method, rooted in the radial point interpolation technique, achieves superior accuracy in predicting piezoelectric behavior compared to the traditional finite element method. This adaptation not only enhances the applicability of meshless modeling but also represents a significant advancement in accurately simulating complex three-dimensional piezoelectric structures.